Journal of Geometry and Physics最新文献

{"title":"A Hamiltonian formalism for general variational problems, with applications to first order gravity with basis","authors":"Guadalupe Quijón ,&nbsp;Santiago Capriotti","doi":"10.1016/j.geomphys.2025.105636","DOIUrl":"10.1016/j.geomphys.2025.105636","url":null,"abstract":"<div><div>The present article introduces a generalization of the (multisymplectic) Hamiltonian field theory for a Lagrangian density, allowing the formulation of this kind of field theories for variational problem of more general nature than those associated to a classical variational problem. It is achieved by realizing that the usual construction of the Hamiltonian equations can be performed without the use of the so called Hamiltonian section, whose existence is problematic when general variational problems are considered. The developed formalism is applied to obtain a novel multisymplectic Hamiltonian field theory for a first order formulation of gravity with basis in the full frame bundle.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"217 ","pages":"Article 105636"},"PeriodicalIF":1.2,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145048347","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The heterotic G2 system with reducible characteristic holonomy","authors":"Mateo Galdeano ,&nbsp;Leander Stecker","doi":"10.1016/j.geomphys.2025.105635","DOIUrl":"10.1016/j.geomphys.2025.105635","url":null,"abstract":"<div><div>We construct solutions to the heterotic G₂ system on almost contact metric manifolds with reduced characteristic holonomy. We focus on 3-<span><math><mo>(</mo><mi>α</mi><mo>,</mo><mi>δ</mi><mo>)</mo></math></span>-Sasaki manifolds and <span><math><mo>(</mo><mi>α</mi><mo>,</mo><mi>δ</mi><mo>)</mo></math></span>-Sasaki manifolds, the latter being a convenient reformulation of spin <em>η</em>-Einstein <em>α</em>-Sasaki manifolds. Investigating a 1-parameter family of G₂-connections on the tangent bundle, we obtain several approximate solutions as well as one new class of exact solutions on degenerate 3-<span><math><mo>(</mo><mi>α</mi><mo>,</mo><mi>δ</mi><mo>)</mo></math></span>-Sasaki manifolds.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"217 ","pages":"Article 105635"},"PeriodicalIF":1.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144931865","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Rigidity theorems on critical metrics for quadratic functionals","authors":"Liyi Cao,&nbsp;Guangyue Huang","doi":"10.1016/j.geomphys.2025.105634","DOIUrl":"10.1016/j.geomphys.2025.105634","url":null,"abstract":"<div><div>By introducing a trace-less symmetric three tensor, we obtain some rigidity results for the Einstein metrics as the critical points of a family of known quadratic curvature functionals on manifolds, which involve the Weyl curvature and the trace-less Ricci curvature.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"217 ","pages":"Article 105634"},"PeriodicalIF":1.2,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144925702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Lorentzian manifolds equipped with a concircularly semi-symmetric metric connection","authors":"Miroslav D. Maksimović ,&nbsp;Milan Lj. Zlatanović ,&nbsp;Milica R. Vučurović","doi":"10.1016/j.geomphys.2025.105633","DOIUrl":"10.1016/j.geomphys.2025.105633","url":null,"abstract":"<div><div>Building upon previous works characterizing GRW space-times using concircular and torse-forming vectors, this paper investigates a Lorentzian manifold equipped with a concircularly semi-symmetric metric connection. We demonstrate that such a manifold reduces to a GRW space-time under specific conditions: when the generator of the observed connection is a unit timelike vector. Also, in that case, the mentioned connection becomes a semi-symmetric metric <em>P</em>-connection. The non-zero nature of the three curvature tensors and their corresponding Ricci tensors motivates an exploration of manifold symmetries. In this way, we derive necessary and sufficient conditions for the manifold to be Einstein and we prove that a perfect fluid space-time with a semi-symmetric metric <em>P</em>-connection is Ricci pseudo-symmetric manifold of constant type. Furthermore, we show that if this space-time satisfies the Einstein's field equations without the cosmological constant, the strong energy condition is violated.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"217 ","pages":"Article 105633"},"PeriodicalIF":1.2,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144922561","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Deformations of calibrated subbundles in noncompact manifolds of special holonomy via twisting by special sections","authors":"Romy Marie Merkel","doi":"10.1016/j.geomphys.2025.105631","DOIUrl":"10.1016/j.geomphys.2025.105631","url":null,"abstract":"<div><div>We study special Lagrangian submanifolds in the Calabi–Yau manifold <span><math><msup><mrow><mi>T</mi></mrow><mrow><mo>⁎</mo></mrow></msup><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> with the Stenzel metric, as well as calibrated submanifolds in the <span><math><msub><mrow><mtext>G</mtext></mrow><mrow><mn>2</mn></mrow></msub></math></span>-manifold <span><math><msubsup><mrow><mi>Λ</mi></mrow><mrow><mo>−</mo></mrow><mrow><mn>2</mn></mrow></msubsup><mo>(</mo><msup><mrow><mi>T</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mi>X</mi><mo>)</mo></math></span> <span><math><mo>(</mo><msup><mrow><mi>X</mi></mrow><mrow><mn>4</mn></mrow></msup><mo>=</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>4</mn></mrow></msup><mo>,</mo><msup><mrow><mi>CP</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> and the <span><math><mtext>Spin</mtext><mo>(</mo><mn>7</mn><mo>)</mo></math></span>-manifold <figure><img></figure>, both equipped with the Bryant–Salamon metrics. We twist naturally defined calibrated subbundles by sections of the complementary bundles and derive conditions for the deformations to be calibrated. We find that twisting the conormal bundle <span><math><msup><mrow><mi>N</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mi>L</mi></math></span> of <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msup><mo>⊂</mo><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> by a 1-form <span><math><mi>μ</mi><mo>∈</mo><msup><mrow><mi>Ω</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><mi>L</mi><mo>)</mo></math></span> does not provide any new examples because the Lagrangian condition requires <em>μ</em> to vanish. Furthermore, we prove that the twisted bundles in the <span><math><msub><mrow><mtext>G</mtext></mrow><mrow><mn>2</mn></mrow></msub></math></span>- and <span><math><mtext>Spin</mtext><mo>(</mo><mn>7</mn><mo>)</mo></math></span>-manifolds are associative (coassociative) and Cayley, respectively, if the base is minimal (negative superminimal) and the section holomorphic (parallel). This demonstrates that the (co-)associative and Cayley subbundles allow deformations destroying the linear structure of the fiber, while the base space remains of the same type after twisting. While the results for the two spaces of exceptional holonomy are in line with the findings in Euclidean spaces established by Karigiannis and Leung (2012), the special Lagrangian bundle construction in <span><math><msup><mrow><mi>T</mi></mrow><mrow><mo>⁎</mo></mrow></msup><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> is much more rigid than in the case of <span><math><msup><mrow><mi>T</mi></mrow><mrow><mo>⁎</mo></mrow></msup><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"217 ","pages":"Article 105631"},"PeriodicalIF":1.2,"publicationDate":"2025-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144911770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Homotopy representations of extended holomorphic symmetry in holomorphic twists","authors":"D. Simon H. Jonsson,&nbsp;Hyungrok Kim,&nbsp;Charles A.S. Young","doi":"10.1016/j.geomphys.2025.105632","DOIUrl":"10.1016/j.geomphys.2025.105632","url":null,"abstract":"<div><div>We argue that holomorphic twists of supersymmetric field theories naturally come with a symmetry <span><math><msub><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span>-algebra that nontrivially extends holomorphic symmetry. This symmetry acts on spacetime fields only up to homotopy, and the extension is only visible at the level of higher components of the action. We explicitly compute this for the holomorphic twist of ten-dimensional supersymmetric Yang–Mills theory, which produces a nontrivial action of a higher <span><math><msub><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span>-algebra on (a graded version) of five-dimensional affine space.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"217 ","pages":"Article 105632"},"PeriodicalIF":1.2,"publicationDate":"2025-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144911769","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A topological quantum field theory for Spin(7)-instantons","authors":"Rafael Herrera ,&nbsp;Sergio A. Holguín Cardona ,&nbsp;Alexander Quintero Vélez","doi":"10.1016/j.geomphys.2025.105630","DOIUrl":"10.1016/j.geomphys.2025.105630","url":null,"abstract":"<div><div>We construct a topological quantum field theory based on the moduli space of <span><math><mi>Spin</mi><mo>(</mo><mn>7</mn><mo>)</mo></math></span>-instantons on 8-dimensional manifolds. Using the Mathai-Quillen formalism, we derive the action of the theory in purely geometric terms, which coincides with prior results in the literature. We then reformulate the theory within the AKSZ formalism, obtaining a Batalin–Vilkovisky action that, after gauge fixing, matches our Mathai-Quillen construction while making the BRST symmetry explicit and providing a natural framework for classical observables. We also show that the Batalin–Vilkovisky action can be elegantly recast as a Chern–Simons type theory.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"217 ","pages":"Article 105630"},"PeriodicalIF":1.2,"publicationDate":"2025-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144911863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Filling Riemann surfaces by hyperbolic Schottky manifolds of negative volume","authors":"Tommaso Cremaschi ,&nbsp;Viola Giovannini ,&nbsp;Jean-Marc Schlenker","doi":"10.1016/j.geomphys.2025.105628","DOIUrl":"10.1016/j.geomphys.2025.105628","url":null,"abstract":"<div><div>We provide conditions under which a Riemann surface <em>X</em> is the asymptotic boundary of a convex co-compact hyperbolic manifold, homeomorphic to a handlebody, of negative renormalized volume. We prove that this is the case when there are on <em>X</em> enough closed curves of short enough hyperbolic length.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"217 ","pages":"Article 105628"},"PeriodicalIF":1.2,"publicationDate":"2025-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144925701","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Local high-degree polynomial integrals of geodesic flows and the generalized hodograph method","authors":"Sergei Agapov","doi":"10.1016/j.geomphys.2025.105629","DOIUrl":"10.1016/j.geomphys.2025.105629","url":null,"abstract":"<div><div>We study Riemannian metrics on 2-surfaces with integrable geodesic flows such that an additional first integral is high-degree polynomial in momenta. This problem reduces to searching for solutions to certain quasi-linear systems of PDEs which turn out to be semi-Hamiltonian. We construct plenty of local explicit and implicit integrable examples with polynomial first integrals of degrees 3, 4, 5. Our construction is essentially based on applying the generalized hodograph method.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"217 ","pages":"Article 105629"},"PeriodicalIF":1.2,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144895920","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Affinization of Alia bialgebras and Lie bialgebras","authors":"Yanhong Guo,&nbsp;Bo Hou","doi":"10.1016/j.geomphys.2025.105627","DOIUrl":"10.1016/j.geomphys.2025.105627","url":null,"abstract":"<div><div>The purpose of this paper is to study the affinization of Alia algebras. We show that the tensor product of an Alia algebra and an infinite-dimensional commutative associative algebra is an infinite-dimensional Alia algebra. This is called an affinization of Alia algebras. We obtain an affinization characterization of Alia coalgebras and lift the affinization of Alia coalgebras to the Alia bialgebras. In particular, we also give the affinization of Lie bialgebras.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"217 ","pages":"Article 105627"},"PeriodicalIF":1.2,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144879606","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}